document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=509370>Question 509370</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The function f is defined by f(x) = x^3\r<BR>\n" );
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document.write( "Find the expression for g(x) in terms of x in each of the following cases\r<BR>\n" );
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document.write( "(a)   f(g(x)) = x + 1<BR>\n" );
document.write( "(b)   g(f(x)) = x + 1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #341403 by </B><A HREF=/tutors/aboutme.mpl?userid=swincher4391><B>swincher4391(1107)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=swincher4391><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=swincher4391><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=341403\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Interesting question.\r<BR>\n" );
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document.write( "Let's figure out what the INVERSE of f(x) is.\r<BR>\n" );
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document.write( "y = x^3<BR>\n" );
document.write( "cbrt stands for cube root or 'third root'<BR>\n" );
document.write( "cbrt(y) = x\r<BR>\n" );
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document.write( "Switch x and y\r<BR>\n" );
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document.write( "y = cbrt(x)\r<BR>\n" );
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document.write( "So if we were to put in cbrt(x) as our g(x), by definition  f(g(x)) = x.\r<BR>\n" );
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document.write( "But we want x+1.\r<BR>\n" );
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document.write( "So we put in cbrt(x+1), and that is our answer for part a.\r<BR>\n" );
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document.write( "Again the inverse of f(x) is cbrt(x).\r<BR>\n" );
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document.write( "So cbrt(f(x)) = x\r<BR>\n" );
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document.write( "We want our end result to be x+1.\r<BR>\n" );
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document.write( "So g(x) must be  cbrt(x) + 1. <--- Part b answer </SPAN>\n" );
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